Grade 5 Math Practice Test: Powers of 10 and Place Value

10³ means 10 × 10 × 10 = 1,000. 30 multiplies 10 by 3 instead of using 3 as an exponent.

10⁴ = 10,000, and 6 × 10,000 = 60,000: four zeros after the 6. 24 multiplies 6 by 4.

Dividing by 10² = 100 moves each digit two places to the right, so 45.7 becomes 0.457. 4,570 multiplies by 100 instead of dividing.

Multiplying by 10³ = 1,000 moves each digit three places to the left: 0.38 → 3.8 → 38 → 380. 38 moves only two places.

The 5 in the hundreds place is worth 500 and the 5 in the tens place is worth 50. 500 ÷ 50 = 10, and each place is 10 times the place to its right.

The 4 in 7.42 is worth 0.4. One tenth of 4 is 0.4, so we need a number where the 4 is worth 4, in the ones place: 74.2. In 742 the 4 is worth 40.

10,000 = 10 × 10 × 10 × 10, which is 10⁴. Counting the zeros in 10,000 gives the exponent 4.

0.08 × 1,000 moves each digit three places to the left: 0.08 → 80, so the stack is 80 millimeters tall. 8 moves the digits only two places.

Undo the multiplication by dividing: 54 ÷ 100 = 0.54. Check: 0.54 × 100 = 54. 5,400 multiplies by 100 again instead of undoing it.

10⁴ = 10,000, and 2.4 × 10,000 = 24,000 gallons. Moving the digits four places left turns 2.4 into 24,000.