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.
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
1 answer
1 answer