Decimals: place value and the powers of ten (Grade 5)

If your child is in Grade 5, the topic "Decimals: place value and the powers of ten" 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 Grade 5 children learn

• Read and write decimals to thousandths and say what each digit is worth
• Compare and order decimals by lining up the places
• Multiply and divide by 10, 100 and 1000 by moving the digits

The key ideas

• Each place is worth 10 times the place to its right: ones, tenths, hundredths, thousandths.
• In 0.704, the 7 is 7 tenths and the 4 is 4 thousandths. The 0 holds the hundredths place.
• To compare decimals, line up the places and add zeros: 0.4 and 0.35 become 0.40 and 0.35, so 0.4 is greater.
• Multiplying by 10, 100 or 1000 moves every digit 1, 2 or 3 places to the left (bigger). Dividing moves them to the right (smaller).
• Use a 0 to fill any empty place: 4 ÷ 100 = 0.04.

Quick examples

• In 6.382 the 3 is 3 tenths (0.3), the 8 is 8 hundredths (0.08) and the 2 is 2 thousandths (0.002)
• 0.5 is greater than 0.45, because 0.50 is 50 hundredths and 0.45 is only 45 hundredths
• 3.07 × 100 = 307
• 45 ÷ 1000 = 0.045

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 "Decimals" 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