Read, write, and compare decimals to thousandths using base-ten numerals, number names, and expanded form; compare using >, =, < based on place-value meaning
You already know tenths, hundredths and thousandths from the stall board and the rain gauge. Now you will read bigger numbers that have whole ones as well as tiny parts. To the left of the point the names stay as they always were: ones, tens, hundreds, growing outwards. To the right, each new place stands for a value ten times smaller than the one before it.
Look at 528.416. The 4 right after the decimal point is 4 tenths, or 0.4. The 1 is 1 hundredth, or 0.01. The 6 is 6 thousandths, or 0.006.
Expanded form adds up the value of every digit: 5x100 + 2x10 + 8x1 + 4x(1/10) + 1x(1/100) + 6x(1/1000) makes 528.416. Each part names one place, and the fraction in it tells you which place.
Word names work the same way. 'And' marks the decimal point, so 'two and forty-seven thousandths' means 2 ones plus 47 thousandths, written as 2.047. There are no tenths in it, so a 0 holds that spot.
To compare decimals, line up the decimal points and check one place at a time, starting from the biggest place. 0.451 and 0.46 tie at 4 tenths, but 0.46 has 6 hundredths while 0.451 only has 5, so 0.46 is larger. Writing 0.46 as 0.460 first lines the places up, and a zero on the end never changes the value.
Read decimals by place value, use 'and' for the decimal point in words, and compare digit by digit starting from the largest place.
Last summer the rain gauge gave you readings to three places after the point. The season ledger wants three places too, with bigger numbers in front. Leo has ruled the top line and written the year's total: 528.416 kilograms weighed and sold at the stall.
In 528.416, what is that last 6 worth?
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.