3.1 Multiplying and dividing by powers of 10 · Unit 3 Place value and rounding

1 · Teaching slidesuse ← → keys

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2 · Key words

power of 10A number made by multiplying 10s together: 10, 100, 1000, …

indexThe small raised number that says how many 10s are multiplied, as in 10⁴.

place valueThe value a digit has because of its position in a number.

decimal pointThe dot that separates the whole-number part from the decimal part.

digitOne of the symbols 0 to 9.

3 · Summary of the sectionrevise from this

10¹ = 10, 10² = 100, 10³ = 1000, 10⁴ = 10 000 — the index is the number of zeros.
Multiplying by 10ⁿ moves every digit n places to the left. The number gets bigger.
Dividing by 10ⁿ moves every digit n places to the right. The number gets smaller.
It is the digits that move, not the decimal point — but moving the point the other way gives the same result, so either picture works.
Fill any empty places with zeros: 4.5 × 10³ = 4500, and 47 ÷ 10³ = 0.047.
“Crossing off zeros” only works if the number has enough zeros to cross off, so it is safer to move the digits.
Always sanity-check: should the answer be bigger or smaller than you started with?