Numbers to ten million
Solve number and practical problems involving reading, writing, ordering, comparing, rounding, and negative numbers up to 10,000,000
What a learner can do afterwards
- Round a reported population to a named place, explain the deciding digit, and find whole-number rounding boundaries
- Interpret, order and compare signed positions relative to sea level, and calculate gaps between them
- Estimate event counts using totals, differences and repeated equal groups; compare an estimate with the exact total
1 · Read
You have rounded whole numbers and decimals before. Here, use rounding with counts up to ten million. Choose the place to keep and check the next digit to its right. If it is 5 or more, add one to the kept place. If it is less than 5, keep that place unchanged. Replace all digits to its right with zeros. A rounded count is an estimate.
A report gives a population of 8,274,500. Round it to the nearest million for a headline. The hundred-thousands digit is 2. Since 2 is less than 5, keep the 8 and replace the remaining digits with zeros: 8,000,000. The headline can say about 8 million people.
Sea level is 0 m. A position of -8,200 m means 8,200 m below sea level. Numbers increase as you move right on a number line. Among negative numbers, the one farther left is smaller. So -8,200 is smaller than -3,400, and -8,200 m is deeper. To order depths from deepest to shallowest, put the most negative value first.
Diving deeper makes a position more negative. A craft at -900 m that dives another 500 m reaches -1,400 m: add 900 + 500 to find its distance below sea level, then keep the negative sign. Rising towards sea level makes a negative position closer to zero.
To estimate a total, round each count first, then add. Counts of 131,000, 286,000 and 424,000 become 100,000, 300,000 and 400,000 to the nearest 100,000. Their estimated total is 800,000. To estimate how many more one event had than another, round both counts to the requested place, then subtract the smaller rounded count from the larger.
To find which whole numbers round to a target, check both halfway points. Numbers from 5,500,000 through 6,499,999 round to 6,000,000 to the nearest million. At 5,500,000, the halfway rule rounds up to 6,000,000. At 6,500,000, it rounds up to 7,000,000. So 6,499,999 is the largest whole number that rounds to 6,000,000.
Rounding can carry into a new place: 9,980,000 rounds to 10,000,000 to the nearest 100,000. Always round the original number directly to the requested place. For example, 5,460,000 rounds directly to 5,000,000 to the nearest million. Rounding it first to 5,500,000, then to a million, gives 6,000,000 instead.
To check whether an estimate is above or below the exact total, add the original counts and compare. For 184,200 + 236,700 + 315,600, the exact total is 736,500. Rounding each to the nearest 100,000 gives 200,000 + 200,000 + 300,000 = 700,000. Here the estimate is smaller. An estimate can also be larger.
For repeated equal counts, round the count before multiplying. To estimate 3 × 428,000 by rounding 428,000 to the nearest 100,000, use 3 × 400,000 = 1,200,000. Think of three groups of four hundred thousands: 3 × 4 = 12 hundred thousands, which is 1,200,000.
For two positions below sea level, subtract their distances below zero to find the vertical gap. Between -4,200 m and -1,600 m, the gap is 4,200 - 1,600 = 2,600 m. If the positions are on opposite sides of zero, add the distances to zero. From -1,600 m to +300 m, the gap is 1,600 + 300 = 1,900 m.
Round by checking the next digit, and remember: the more negative a number is, the smaller it is.
Readings and practice questions written for this dataset. Flashcards explain mathematical facts.
More to read
Checking a large number in a report
Suppose a report gives a count of 6,083,040. The groups are 6 million, 83 thousand and 40. The 8 has a value of 80,000; the 4 has a value of 40.
A second report gives 6,080,340. Compare from the left. The millions and thousands groups match until the thousands digit: 3 is greater than 0. So 6,083,040 is greater. Matching digits near the start do not mean the whole numbers are equal.
Zeros hold a place
Write seven million, four thousand, sixty-two in digits. Begin with three groups: 7 | 004 | 062. The groups after millions each need three digits. Join them to get 7,004,062.
The zeros keep the 4 in the thousands place and the 6 in the tens place. When reading the number aloud, do not say each zero. In 7,000,062, the entire thousands group is zero, so say seven million, sixty-two.
Choosing how much detail to report
Imagine a visitor count of 2,738,600. Rounded to the nearest million, it is 3,000,000. Rounded to the nearest hundred thousand, it is 2,700,000. Both are estimates of the same count, using different rounding places.
Name the rounding place when reporting an estimate. Keep the exact count when every visit matters. If you estimate a total, round each count to the requested place before adding. The estimate may be above or below the exact total.
2 · Watch
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Where it sits
Where this leads
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.