Question

Show that between any two terminating decimals, there is another terminating decimal between:

a) 0.1 and 0.2
b) 0.5 and 0.6
c) 0.9 and 1.0
d) 1.2 and 1.3

Answer 1

To show that between any two terminating decimals, there is another terminating decimal between them, you can convert the decimals to fractions and find a fraction between them by taking the average. This fraction can then be converted back to a decimal.

Step-by-step explanation:

To show that between any two terminating decimals, there is another terminating decimal between them, we can use the fact that any terminating decimal can be expressed as a fraction with a power of 10 in the denominator. Let's take the example of a) 0.1 and 0.2:

1. Convert both 0.1 and 0.2 to fractions: 0.1 = 1/10 and 0.2 = 2/10.
2. Find a fraction between 1/10 and 2/10 by taking the average: (1/10 + 2/10)/2 = 3/20.
3. Convert 3/20 back to a decimal: 3/20 = 0.15.

Therefore, a decimal between 0.1 and 0.2 is 0.15. You can follow the same steps for b) 0.5 and 0.6, c) 0.9 and 1.0, and d) 1.2 and 1.3 to find decimals between these pairs.