Curriculum placement
Grade 5. This describes the skill, not a learner estimate.
Powers of 10 and place value
Explain place-value shifts when multiplying by powers of ten
Problem types
- Multiply or divide by 0.1 and 0.01
- Multiply by 10, 100 or 1,000
- Divide by 10, 100 or 1,000
- Compare two places of the same digit
Builds on
- Tenths and hundredths as decimals
- Place value of large whole numbers
- Decimal place value through thousandths · Useful idea
Every place in a number is ten times the place to its right, so the place values 1,000, 100, 10, 1, 0.1 and 0.01 are powers of ten. Writing a number as digit-times-place-value sums is the base for multiplying and dividing by powers of ten.
- Converting to a smaller unit · Useful idea
Metric prefixes are powers of ten, so converting units is multiplying or dividing by a power of ten.
- Multiplying by a multiple of 10 · Earlier idea
Multiplying by 10, 100 or 1000 shifts each digit left by that many places, which is the multiplication by powers of ten.
- Adding or subtracting 10 or 100 mentally · Earlier idea
Shifting a value by ten or one hundred in place value becomes multiplying and dividing by powers of ten.
Leads to
- Whole-number powers
- Laws of exponents · Extend the idea
Multiplying 10 to the power a by 10 to the power b gives 10 to the power a + b, the first exponent law, shown with place value.
- Working in scientific notation · Extend the idea
Multiplying and dividing by powers of ten shifts digits, and scientific notation writes any number as a digit string times one power of ten.
Related skills
- Comparing decimals to hundredths · Shared foundations
- Money with decimals · Shared foundations
- Dividing by a one-digit number · Shared foundations
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