Place value and powers of 10 (grade 5) · lesson

Powers of 10

💡 The small raised number tells how many 10s to multiply together.

10⁵ means 10 × 10 × 10 × 10 × 10. That is 100,000.

The raised number is the number of zeros after the 1. It does not mean multiply by that number.

A number times a power of 10 works the same way. 4 × 10² is 4 × 100 = 400.

🧠 Let's work it out

Find 10⁵.

What do you think comes next?

exponent: the small raised number that tells how many times to multiply
power of 10: 10 multiplied by itself some number of times, like 100 or 1,000

💡 Multiplying by 10 moves every digit one place to the left.

Each place is worth 10 times the place to its right. So times 10 moves each digit one place left.

Times 100 moves digits two places. Times 1,000 moves them three places. Times 10⁴ moves them four places: the exponent tells how many.

🧠 Let's work it out

Find 3.6 × 100.

What do you think comes next?

💡 Dividing by 10 moves every digit one place to the right.

Divide by 10 and each digit moves one place right. Divide by 100 and they move two places.

You may need zeros to hold places. 8 ÷ 1,000 is 0.008.

🧠 Let's work it out

Find 47 ÷ 100.

What do you think comes next?

💡 A digit is worth ten times as much as the same digit one place to its right.

In 3.33 the tenths 3 is worth 0.3. The hundredths 3 is worth 0.03.

0.3 is ten times 0.03. This is true for any two places side by side.

🧠 Let's work it out

In 7.77, how many times is the ones 7 worth the tenths 7?

What do you think comes next?

💡 To round a decimal, look at the digit just to the right of the place you round to.

To round to the nearest tenth, look at the hundredths digit. To round to the nearest hundredth, look at the thousandths.

5 or more rounds up. 4 or less rounds down. Drop the digits after the place you round to.

🧠 Let's work it out

Round 6.274 to the nearest tenth.

What do you think comes next?