Place value to the millions and thousandths, then large numbers

If your child is working on Grades 5 and 6 math, the topic "Place value to the millions and thousandths, then large numbers" is one of the ideas where confidence is most often won or lost. Here is what it means in plain words, a worked example you can follow together, and a few simple ways to help at home.

What Grades 5 and 6 children learn

• Read, write and say whole numbers into the millions and decimals to thousandths, using place value
• See that each place is 10 times the place to its right, and multiply or divide by 10, 100 and 1000 by moving the digits
• Write numbers in expanded form, then compare, order and round them

The key ideas

• Each place is worth 10 times the place to its right. Past the ones the places shrink: tenths, hundredths, thousandths.
• A digit is worth the digit times its place: in 3 405 072 the 4 means 4 × 100 000 = 400 000. A zero holds a place so the other digits stay where they belong.
• Multiply by 10, 100 or 1000 and every digit moves 1, 2 or 3 places left. Divide and the digits move right.
• To compare decimals, write them with the same number of places (0.5 = 0.500) and compare from the left.
• To round, find the place, then look at the digit to its right: 5 or more rounds up, 4 or less stays.

Quick examples

• 3 405 072 is three million, four hundred five thousand, seventy-two, and the 4 is worth 400 000; in expanded form 52 308.075 = 50 000 + 2000 + 300 + 8 + 0.07 + 0.005 (the zero places add nothing)
• Order 0.6, 0.59 and 0.509 from least to greatest: write them to thousandths (0.600, 0.590, 0.509), so the order is 0.509, 0.59, 0.6
• Round 2 468 395 to the nearest ten thousand: the ten-thousands digit is 6 and the digit to its right is 8 (5 or more), so round up to 2 470 000
• 0.38 × 1000 = 380 and 52.6 ÷ 100 = 0.526 (for × 1000 each digit moves 3 places to the left; for ÷ 100 each digit moves 2 places to the right)

A worked example

How to help at home

• Ask your child to explain the first step of the worked example in their own words before you show them anything.
• Work through the "Try it yourself" question together, and talk about why the answer makes sense.
• Spend a few minutes a day on the free Tutorizer "Place value" practice. Short and regular beats long and rare.
• If a step feels shaky, go back to the key ideas above and use objects, drawings or a number line.

Try it yourself

Want a challenge?

Next steps