Study guide: Read, Scale, Compare, and Round Decimals
Extend place value through thousandths and explain powers-of-ten changes.
Ideas to explain in your own words
- Decimals extend the base-ten pattern to places smaller than a whole.
- Multiplying by ten makes every place value ten times larger; dividing by ten makes it one tenth as large.
- Decimal comparison uses equally sized places from left to right.
- Decimal rounding uses the same nearest-landmark idea as whole-number rounding.
Useful vocabulary
- thousandth
- One of one thousand equal parts of a whole.
- power of ten
- A value such as 10,100,1000 formed from repeated factors of ten.
Watch your reasoning
- A digit in thousandths is ten times smaller than the same digit in hundredths.
- Check the scaling direction rather than memorizing an unexamined dot movement.
- Do not compare decimal strings by digit count.
- Rounding an already rounded value can differ from rounding the original directly.
A worked review example
The number 4.307 is four ones, three tenths, zero hundredths, and seven thousandths. Expanded form is 4+0.3+0.007. Its fractional part is 307/1000. Writing 4.37 would move the seven into hundredths and change the value. Write a zero for an empty place between occupied places. A digit in thousandths is ten times smaller than the same digit in hundredths. Make Ones, Tenths, Hundredths, and Thousandths columns.
Make a practice plan
- Read Decimal Place Values through Thousandths: Expand 6.052. Expected: 6+0.05+0.002.
- Explain Decimal Scaling by Powers of Ten: Calculate 0.735×100 and 73.5÷100. Expected: 73.5 and 0.735.
- Compare Decimals by the First Unequal Place: Compare 5.050 and 5.05. Expected: equal.
- Round Decimals to a Requested Place: Round 9.996 to hundredths. Expected: 10.00, including the carry into a new whole.