How place value works with decimals: each place is worth ten times the place to its right and a tenth of the place to its left, so × 10 and ÷ 10 shift the digits.
Multiplying by 10 moves each digit one place left, so it's worth ten times as much. Dividing by 10 moves each digit one place right: 4 ÷ 10 = 0.4.
tenthone of 10 equal parts: 0.1
hundredthone of 100 equal parts: 0.01
thousandthone of 1,000 equal parts: 0.001
place valuewhat a digit is worth from where it sits
Watch for: Just adding a zero to a decimal: 0.3 × 10 is 3, not 0.30. Moving the digits the wrong way when dividing: 4 ÷ 10 is 0.4, not 40. Writing the digit instead of its value: in 83.923 the 2 is worth 0.02.
At home: Use money: a dime is a tenth of a dollar and a penny is a tenth of a dime. How many dimes make $1? How many pennies make a dime?
Sample sheet and answer key
Luna's Space Adventure
Grade 5 · Place value with decimals · 5.NBT.A.1
NameDate
Astronaut Luna is exploring a far-off corner of space. Solve each problem to help Luna's mission go smoothly!
Ten times and a tenth
One place left is ten times as much; one place right is a tenth.
New problems every time, three levels (gentle, core and stretch), themes to pick from, a second page if you want one. Each sheet comes with an answer key and a one-page guide for grown-ups.
