Question

multiplying powers of 10
steps:

1. count the zeros in the power of 10.
2. move the decimal that many places to the right. (add zeros as place holders if needed.)
3. answer

example 1: $10 \times 8.5$
$10$ (one zero)
$8.5$
$85$
example 2: $6.42 \times 1000$
$1000$
$6.420$
$6,420$
$6.57 \times 10$
$1,000 \times 1.5$
$100 \times 52.6$
$10 \times 8.2$
$100 \times 9.708$
$1,000 \times 6.1$
$10,000 \times 7.4$
$28.01 \times 10$
$1,000 \times 0.32$
$44.05 \times 100$
$10 \times 0.05$
$100 \times 72.4$
humble

Explanation:

Step1: Count zeros in power of 10

For each problem, identify the number of zeros in the power of 10 (10 has 1 zero, 100 has 2, 1000 has 3, 10000 has 4).

Step2: Move decimal right by that count

Shift the decimal point of the other number to the right by the number of zeros; add zeros if needed.

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For problems ①-④:

Step1: 10 has 1 zero

$6.57 \times 10$: Move decimal 1 right.
$1,000 \times 1.5$: 1000 has 3 zeros, move decimal 3 right.
$100 \times 52.6$: 100 has 2 zeros, move decimal 2 right.
$10 \times 8.2$: 10 has 1 zero, move decimal 1 right.

Step2: Calculate each result

$6.57 \to 65.7$; $1.5 \to 1500$; $52.6 \to 5260$; $8.2 \to 82$

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For problems ⑨-⑫:

Step1: Count zeros in power of 10

$100 \times 9.708$ (2 zeros); $1,000 \times 6.1$ (3 zeros); $10,000 \times 7.4$ (4 zeros); $28.01 \times 10$ (1 zero)

Step2: Shift decimals

$9.708 \to 970.8$; $6.1 \to 6100$; $7.4 \to 74000$; $28.01 \to 280.1$

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For problems ⑬-⑯:

Step1: Count zeros in power of 10

$1,000 \times 0.32$ (3 zeros); $44.05 \times 100$ (2 zeros); $10 \times 0.05$ (1 zero); $100 \times 72.4$ (2 zeros)

Step2: Shift decimals

$0.32 \to 320$; $44.05 \to 4405$; $0.05 \to 0.5$; $72.4 \to 7240$

Answer:

① $65.7$
② $1500$
③ $5260$
④ $82$
⑨ $970.8$
⑩ $6100$
⑪ $74000$
⑫ $280.1$
⑬ $320$
⑭ $4405$
⑮ $0.5$
⑯ $7240$