---
title: "Number Representation & Place Value"
description: "59 topics in Mathematics, in the order they build on each other."
canonical: https://lightmysky.com/learn/mathematics/areas/number-representation-and-place-value
source: https://lightmysky.com/learn/mathematics/areas/number-representation-and-place-value.md
retrieved: 2026-10-19
---

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# Number Representation & Place Value

59 topics in Mathematics, in the order they build on each other.

Page: https://lightmysky.com/learn/mathematics/areas/number-representation-and-place-value

- [Reading and writing numbers to 20](https://lightmysky.com/learn/mathematics/reading-and-writing-numbers-to-20-mt_fR0UtsSREU): Read and write numerals from 0 to 20
- [Number Words to Twenty](https://lightmysky.com/learn/mathematics/number-words-to-twenty-mt_9IzhGUZ30z): Read and write number words from one to twenty
- [Reading and writing numbers to 100](https://lightmysky.com/learn/mathematics/reading-and-writing-numbers-to-100-mt_x8TshvbbQT): Read and write numerals from 0 to 100
- [The teen numbers](https://lightmysky.com/learn/mathematics/the-teen-numbers-mt_xmmgAzxe5j): Understand that the teen numbers (11–19) are composed of ten ones and some further ones (early place value)
- [A Ten Is Ten Ones](https://lightmysky.com/learn/mathematics/a-ten-is-ten-ones-mt_r0VXbfAmsH): Understand that 10 can be thought of as a bundle of ten ones, called a 'ten'
- [Number Words to 100](https://lightmysky.com/learn/mathematics/number-words-to-100-mt_76SPWvdI7r): Read and write numbers to at least 100 in words
- [Reading and writing numbers to 120](https://lightmysky.com/learn/mathematics/reading-and-writing-numbers-to-120-mt_XV0B4kWwqL): Count to 120 starting at any number less than 120; read and write numerals to 120
- [The multiples of 10](https://lightmysky.com/learn/mathematics/the-multiples-of-10-mt_zfy1gOEewd): Understand that the multiples of 10 (10, 20, 30 … 90) represent one to nine tens and 0 ones
- [The two digits of a two-digit number](https://lightmysky.com/learn/mathematics/the-two-digits-of-a-two-digit-number-mt_THl9GLxwoL): Understand that the two digits of a two-digit number represent amounts of tens and ones
- [10 More or 10 Less](https://lightmysky.com/learn/mathematics/10-more-or-10-less-mt_kw7xmp68rU): Mentally find 10 more or 10 less than a given two-digit number without counting
- [Comparing and ordering numbers](https://lightmysky.com/learn/mathematics/comparing-and-ordering-numbers-mt_U0waNfD8PB): Compare and order two-digit numbers using the symbols >, =, and <, based on place value understanding
- [Place value understanding and number facts](https://lightmysky.com/learn/mathematics/place-value-understanding-and-number-facts-mt_kJGCjnuelW): Use place value understanding and number facts to solve problems
- [A Hundred Is Ten Tens](https://lightmysky.com/learn/mathematics/a-hundred-is-ten-tens-mt_8gy7uxRlF6): Understand that 100 can be thought of as a bundle of ten tens, called a 'hundred'
- [Odd or Even](https://lightmysky.com/learn/mathematics/odd-or-even-mt_hniI4E-OCE): Determine whether a group of objects (up to 20) has an odd or even number of members
- [The multiples of 100](https://lightmysky.com/learn/mathematics/the-multiples-of-100-mt_R2ccrI-nKD): Understand that the multiples of 100 (100–900) each represent a number of hundreds with 0 tens and 0 ones
- [The three digits of a three-digit number](https://lightmysky.com/learn/mathematics/the-three-digits-of-a-three-digit-number-mt_aPBzD28_mT): Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones
- [Representing Numbers](https://lightmysky.com/learn/mathematics/representing-numbers-mt_9L3NQqgqRd): Identify, represent, and estimate numbers using different representations including the number line
- [10 or 100 More or Less](https://lightmysky.com/learn/mathematics/10-or-100-more-or-less-mt_izien3ZX51): Find 10 or 100 more or less than a given number up to 1000
- [Ordering Numbers to 1000](https://lightmysky.com/learn/mathematics/ordering-numbers-to-1000-mt_AQcVRBddko): Compare and order numbers up to 1000 using >, =, and < symbols, based on place-value understanding
- [Place Value to 1000](https://lightmysky.com/learn/mathematics/place-value-to-1000-mt_98c2qwEF7Q): Solve number problems and practical problems involving place value of numbers up to 1000
- [Reading and writing numbers to 1000](https://lightmysky.com/learn/mathematics/reading-and-writing-numbers-to-1000-mt_VFsuftfvYM): Read and write numbers to 1000 in numerals, number names, and expanded form
- [Negative Numbers](https://lightmysky.com/learn/mathematics/negative-numbers-mt_vXRzMbiPff): Count backwards through zero to include negative numbers
- [Place value of each digit](https://lightmysky.com/learn/mathematics/place-value-of-each-digit-mt_jY7uf0Cb7o): Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
- [1000 More or Less](https://lightmysky.com/learn/mathematics/1000-more-or-less-mt_9XVFje6Tyr): Find 1000 more or less than a given number
- [Numbers to 10,000](https://lightmysky.com/learn/mathematics/numbers-to-10-000-mt_lC_Q5mSL_I): Identify, represent, and estimate numbers up to 10,000 using different representations
- [Comparing Large Numbers](https://lightmysky.com/learn/mathematics/comparing-large-numbers-mt_MHaiUd2FLA): Order and compare numbers beyond 1000
- [Roman numerals to 100](https://lightmysky.com/learn/mathematics/roman-numerals-to-100-mt_MewIRdzpzz): Read Roman numerals to 100 (I to C) and understand that the numeral system changed over time to include zero and place value
- [Rounding to 10, 100, 1000](https://lightmysky.com/learn/mathematics/rounding-to-10-100-1000-mt_NLSfvB9vUl): Round any number to the nearest 10, 100, or 1000
- [Place Value Problem-Solving](https://lightmysky.com/learn/mathematics/place-value-problem-solving-mt__sMrmOv3bx): Solve number and practical problems involving place value with increasingly large positive numbers
- [Place Value × 10 Pattern](https://lightmysky.com/learn/mathematics/place-value-10-pattern-mt_QqG6IdmTSE): Recognise that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g. 700 ÷ 70 = 10)
- [Counting forwards and backwards (age 9+)](https://lightmysky.com/learn/mathematics/counting-forwards-and-backwards-age-9-mt_tAtMET4EIU): Count forwards and backwards in steps of powers of 10 (10, 100, 1000, 10,000, 100,000) for any given number up to 1,000,000
- [Negative numbers in context](https://lightmysky.com/learn/mathematics/negative-numbers-in-context-mt_1KkvzwYxbR): Interpret negative numbers in context (temperature, sea level, bank balance); count forwards and backwards with positive and negative whole numbers, including through zero
- [Reading and writing numbers (age 9+)](https://lightmysky.com/learn/mathematics/reading-and-writing-numbers-age-9-mt_JwP9QFv6gQ): Read, write, order, and compare whole numbers up to at least 1,000,000 using base-ten numerals, number names, expanded form, and place-value understanding
- [Roman numerals to 1000](https://lightmysky.com/learn/mathematics/roman-numerals-to-1000-mt_To9HdLy8vq): Read Roman numerals to 1000 (M) and recognise years written in Roman numerals
- [Rounding Large Numbers](https://lightmysky.com/learn/mathematics/rounding-large-numbers-mt_5NwqN6pf_A): Round any whole number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000, or 100,000 using place-value understanding
- [Working with Large Numbers](https://lightmysky.com/learn/mathematics/working-with-large-numbers-mt_xMt1TLTs--): Solve number and practical problems involving reading, writing, ordering, comparing, and rounding whole numbers up to 1,000,000
- [Negative Numbers Across Zero](https://lightmysky.com/learn/mathematics/negative-numbers-across-zero-mt_RVK655t391): Use negative numbers in context (temperature, finance, sea level); calculate intervals across zero
- [Integer powers and roots](https://lightmysky.com/learn/mathematics/integer-powers-and-roots-mt_hCVPYlF-7Y): Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations
- [Number Sets & Infinity](https://lightmysky.com/learn/mathematics/number-sets-and-infinity-mt_b4lbTOJYwI): Appreciate the infinite nature of the sets of integers, real numbers, and rational numbers; position integers on a number line and distinguish between rational and irrational numbers
- [Recurring Decimals as Exact Fractions](https://lightmysky.com/learn/mathematics/recurring-decimals-as-exact-fractions-mt_Mb-sXIZDWd): A decimal that repeats forever is still an exact fraction, and multiplying by a power of ten before subtracting is what pins it down. This is the step that makes the claim about rational numbers repeating into something a learner can act on rather than believe.
- [Place Value × 10 and ÷ 10](https://lightmysky.com/learn/mathematics/place-value-10-and-10-mt_EDgw64OmfA): Recognise that in a multi-digit number, a digit in one place represents 10 times as much as in the place to its right and 1/10 of what it represents in the place to its left
- [Patterns with Powers of Ten](https://lightmysky.com/learn/mathematics/patterns-with-powers-of-ten-mt_HLUqHJ9Y7n): Explain patterns in zeros when multiplying by powers of 10 and in decimal-point placement when multiplying/dividing by a power of 10; use whole-number exponents to denote powers of 10 (e.g. 10³ = 1000)
- [Reading and writing numbers (age 10+)](https://lightmysky.com/learn/mathematics/reading-and-writing-numbers-age-10-mt_Ac7oMWhyPw): Read, write, and compare decimals to thousandths using base-ten numerals, number names, and expanded form; compare using >, =, < based on place-value meaning
- [Reading and writing numbers to 10,000,000](https://lightmysky.com/learn/mathematics/reading-and-writing-numbers-to-10-000-000-mt_Gag_h98jWP): Read, write, order, and compare numbers up to 10,000,000 and determine the value of each digit
- [Reading Decimal Places](https://lightmysky.com/learn/mathematics/reading-decimal-places-mt_lNGpnILM5C): Identify the value of each digit in numbers given to three decimal places (e.g. in 4.378, the 7 represents 7 hundredths)
- [Rounding to a required degree of accuracy](https://lightmysky.com/learn/mathematics/rounding-to-a-required-degree-of-accuracy-mt__casygEB85): Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy
- [Numbers to ten million](https://lightmysky.com/learn/mathematics/numbers-to-ten-million-mt_XNmGwNggdU): Solve number and practical problems involving reading, writing, ordering, comparing, rounding, and negative numbers up to 10,000,000
- [Absolute value as distance from zero](https://lightmysky.com/learn/mathematics/absolute-value-as-distance-from-zero-mt_RWUY7_IXvw): Understand the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as magnitude in real-world contexts; distinguish absolute value comparisons from ordering statements
- [Place value for decimals, measures and integers](https://lightmysky.com/learn/mathematics/place-value-for-decimals-measures-and-integers-mt_PsylzZ9lHW): Understand and use place value for decimals, measures, and integers of any size; extend the number system to include all positive and negative integers, decimals, and fractions on a single number line
- [Order integers, decimals and fractions on a number line](https://lightmysky.com/learn/mathematics/order-integers-decimals-and-fractions-on-a-number-line-mt_uDJY0X0hgo): Order positive and negative integers, decimals, and fractions on a number line; use the symbols =, ≠, <, >, ≤, ≥ to compare values including negative numbers and mixed representations
- [Rounding to decimal places and significant figures](https://lightmysky.com/learn/mathematics/rounding-to-decimal-places-and-significant-figures-mt_U9sme87C32): Round numbers and measures to an appropriate degree of accuracy, including a specified number of decimal places or significant figures.
- [Powers of Ten Notation](https://lightmysky.com/learn/mathematics/powers-of-ten-notation-mt_bO-njVOige): Interpret and compare positive numbers in standard form A × 10ⁿ, where 1 ≤ A < 10 and n is an integer; convert between ordinary notation and standard form
- [Zero and Negative Indices](https://lightmysky.com/learn/mathematics/zero-and-negative-indices-mt_jAtXBSVqkj): Extend the index laws so that any non-zero number to the power 0 is 1 and a negative index means the reciprocal.
- [Fractional Indices and Roots](https://lightmysky.com/learn/mathematics/fractional-indices-and-roots-mt_fdK-nbQcBu): Read x^(1/n) as the nth root and x^(m/n) as a root and a power together, and move between root form and index form.
- [Standard Form](https://lightmysky.com/learn/mathematics/standard-form-mt_GbZZ2xjBTt): Write very large and very small numbers as a number between 1 and 10 times a power of ten, and calculate with them by hand and on a calculator.
- [Surds: Simplifying and Rationalising](https://lightmysky.com/learn/mathematics/surds-simplifying-and-rationalising-mt_cqr0crUUXS): Simplify surds by taking out square factors, add and multiply them, and clear a surd from the bottom of a fraction.
- [Bounds and error in rounded values](https://lightmysky.com/learn/mathematics/bounds-and-error-in-rounded-values-mt_VVn1IXjkzn): Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ b; understand upper and lower bounds of rounded values
- [Upper and Lower Bounds](https://lightmysky.com/learn/mathematics/upper-and-lower-bounds-mt_HaoOqujpRU): Give the upper and lower bounds of a rounded measurement and write the error interval, using the half-unit rule for the accuracy stated.
- [Calculating with Bounds in Compound Measures](https://lightmysky.com/learn/mathematics/calculating-with-bounds-in-compound-measures-mt_zfMz7x8dlf): Combine bounds in a calculation by picking the values that give the greatest and least results, including for speed, density and other compound measures.