Question

common core standard—5.nbt.2
understand the place value system.

1. $10^0 \times 0.23 = $

$10^1 \times 0.23 = $
$10^2 \times 0.23 = $
$10^3 \times 0.23 = $

1. $1 \times 9,670 = $

$0.1 \times 9,670 = $
$0.01 \times 9,670 = $

1. $1 \times 5 = $

$0.1 \times 5 = $
$0.01 \times 5 = $

Explanation:

Step1: Evaluate $10^0 \times 0.23$

Any number to power 0 is 1.
$10^0 \times 0.23 = 1 \times 0.23 = 0.23$

Step2: Evaluate $10^1 \times 0.23$

$10^1=10$, shift decimal right 1.
$10^1 \times 0.23 = 10 \times 0.23 = 2.3$

Step3: Evaluate $10^2 \times 0.23$

$10^2=100$, shift decimal right 2.
$10^2 \times 0.23 = 100 \times 0.23 = 23$

Step4: Evaluate $10^3 \times 0.23$

$10^3=1000$, shift decimal right 3.
$10^3 \times 0.23 = 1000 \times 0.23 = 230$

Step5: Evaluate $1 \times 9,670$

Any number ×1 is itself.
$1 \times 9,670 = 9,670$

Step6: Evaluate $0.1 \times 9,670$

$0.1=\frac{1}{10}$, shift decimal left 1.
$0.1 \times 9,670 = 967.0$

Step7: Evaluate $0.01 \times 9,670$

$0.01=\frac{1}{100}$, shift decimal left 2.
$0.01 \times 9,670 = 96.70$

Step8: Evaluate $1 \times 5$

Any number ×1 is itself.
$1 \times 5 = 5$

Step9: Evaluate $0.1 \times 5$

$0.1=\frac{1}{10}$, shift decimal left 1.
$0.1 \times 5 = 0.5$

Step10: Evaluate $0.01 \times 5$

$0.01=\frac{1}{100}$, shift decimal left 2.
$0.01 \times 5 = 0.05$

Answer:

Problem 3:

$10^0 \times 0.23 = 0.23$
$10^1 \times 0.23 = 2.3$
$10^2 \times 0.23 = 23$
$10^3 \times 0.23 = 230$

Problem 6:

$1 \times 9,670 = 9,670$
$0.1 \times 9,670 = 967.0$
$0.01 \times 9,670 = 96.70$

Problem 9:

$1 \times 5 = 5$
$0.1 \times 5 = 0.5$
$0.01 \times 5 = 0.05$