Grades Fifth Grade Base Ten OperationsMultiplying and Dividing by Powers of 10

Multiplying and Dividing by Powers of 10

🔟 Base Ten Operations

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Multiplying and Dividing by Powers of 10

Each power of 10 shifts every digit exactly one place — the decimal point "moves"!

A POWER OF 10 is 10 raised to a whole-number exponent: 10¹=10, 10²=100, 10³=1,000. Multiplying by a power of 10 shifts all digits LEFT (the number grows). Dividing by a power of 10 shifts all digits RIGHT (the number shrinks). The number of places shifted equals the exponent.

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Multiplying by 10ⁿ → digits shift n places LEFT (bigger number). Dividing by 10ⁿ → digits shift n places RIGHT (smaller number).

✖️Multiplying by powers of 10

2.45 × 10    = 24.5     (shift 1 place left)
2.45 × 100   = 245      (shift 2 places left)
2.45 × 1,000 = 2,450    (shift 3 places left)

The decimal point appears to move RIGHT!

➗Dividing by powers of 10

365 ÷ 10    = 36.5     (shift 1 place right)
365 ÷ 100   = 3.65     (shift 2 places right)
365 ÷ 1,000 = 0.365    (shift 3 places right)

The decimal point appears to move LEFT!

Pattern: 4.7 × powers of 10

4.7 × 10¹ = 474.7 × 10² = 4704.7 × 10³ = 4,7004.7 × 10⁴ = 47,000

Each multiplication by 10 adds one more place to the left — the number grows 10× each time.

2.45 \times 10^3 = 2{,}450 \qquad 365 \div 10^2 = 3.65

How to multiply or divide by a power of 10:

1Count the exponent (or zeros in the power of 10)

2That is how many places the digits shift

3Multiplying: shift digits LEFT (or move decimal point RIGHT)

4Dividing: shift digits RIGHT (or move decimal point LEFT)

5Add placeholder zeros if necessary

✏️ Try It!

What is 0.037 × 1,000?

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Remember This!

Quick check: after multiplying by a power of 10, the answer should be BIGGER than the original. After dividing, it should be SMALLER. If not, you moved the decimal the wrong way!

Practice with CalcVerse

🏗️Place Value Explorer

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