Question

Terminating Decimal to a fraction - RATIONAL- define

Repeating Decimal to a fraction - RATIONAL- define
Non-terminating and non-repeating decimal - IRRATIONAL- define

Answer 1

[AI-generated answer — Bot GPT 3.5]

A terminating decimal is a decimal number that ends after a certain number of digits and does not have any repeating patterns. It can be expressed as a fraction of two integers.

A repeating decimal is a decimal number that has a repeating pattern of digits after the decimal point. It can also be expressed as a fraction of two integers.

An irrational number is a number that cannot be expressed as a fraction of two integers. It is a non-terminating and non-repeating decimal, meaning it goes on forever without any pattern or repetition in its digits. Examples of irrational numbers include √2, π, and e.

Answer 2

Isaac knows that ¼ is written as 0.25 in decimal form. How can he find a decimal for 7/5? Show your work

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the decimal form of 7/5, you can divide the numerator (7) by the denominator (5).

First, set up the division problem:

1.4 (This is the initial estimate of the decimal)
_________
5 | 7.0

Next, divide 7 by 5:
- The quotient is 1, so write 1 above the division symbol.
- Multiply 1 by 5: 1 * 5 = 5.
- Subtract 5 from 7 to get the remainder: 7 - 5 = 2.

To continue, bring down the next digit from the decimal form:

1.4
_________
5 | 7.0
- 5
_________
2

Now, divide 20 (the new dividend) by 5 (the divisor):
- The quotient is 4, so write 4 next to the 1.4.
- Multiply 4 by 5: 4 * 5 = 20.
- Subtract 20 from 20 to get the remainder: 20 - 20 = 0.

Since the remainder is 0, there are no more digits to bring down. Therefore, we have reached the end of the division process.

The final quotient is 1.4 (or 1.40 if you prefer to include the trailing zero). Hence, 7/5 can be written as 1.4 in decimal form.

Answer 4

Explain why a decimal for ⅓ is called a repeating decimal.