use mental math to decide which equations are true, and false, explain you answer
1.23 divided by 10 to the power of 1 = 0.123
123 divided by 100= 1.23
12.3 divided by 10 to the power of 0 = 1.23
0.123 divided by 10 = 1.23
1,230 divided by 10 to the power of 3 =1.23
Let's evaluate each equation using mental math:
1. \(23 \div 10^1 = 0.123\)
This is true because 10 to the power of 1 is 10, and when you divide 23 by 10, you move the decimal point one place to the left, which indeed gives us 2.3. The statement, however, has a mistake; it should be 2.3 and not 0.123.
2. \(123 \div 100 = 1.23\)
This is true because dividing by 100 means moving the decimal point two places to the left. Starting from 123.0, you would get 1.23.
3. \(12.3 \div 10^0 = 1.23\)
This is false. Any number to the power of 0 is 1 (except 0 itself), so dividing 12.3 by 1 would still give us 12.3, not 1.23.
4. \(0.123 \div 10 = 1.23\)
This is false. When you divide 0.123 by 10, you move the decimal point one place to the left, which gives you 0.0123, not 1.23.
5. \(1,230 \div 10^3 = 1.23\)
This is true. 10 to the power of 3 is 1000, and when you divide 1,230 by 1000, you move the decimal point three places to the left, which gives you 1.23.
So, except for the first statement (which has a typo) and the third and fourth statements, which are false, the second and fifth statements are true.