**repeating decimal**is a

**decimal**whose digits

**repeat**. An

**infinite**geometric

**series**is a

**series**of numbers that goes on forever that has the same constant ratio between all successive numbers. All

**repeating decimals**can be rewritten as an

**infinite**geometric

**series**of this form: a + ar + ar2 + ar3 + …

In this regard, how do you know when a decimal is repeating?

Just divide the numerator by the denominator . If you end up with a remainder of 0 , then you have a terminating **decimal**. Otherwise, the remainders will begin to **repeat** after some point, and you have a **repeating decimal**.

Likewise, is 0.25 terminating or repeating? For example, 1/4 is less than one and so is 2500/9999. The decimal number for these fractions will either be a **terminating** decimal or a **repeating** decimal. If we divide 1 by 4 we get **0.25** followed by as many 0's as we'd like. This is a **terminating** decimal number.

Also Know, what do you put over a repeating decimal?

**Repeating decimals are** numbers that continue after the **decimal**, such as .356(356) ¯. The horizontal line, called the vinculum, is usually written **above** the **repeating** pattern of digits. The easiest and most precise way to **add repeating decimals** is to turn the **decimal** into a fraction.

What is 0.123 repeating as a fraction?

We first let **0.123** (123 being repeated) be x . Since x is **recurring** in 3 decimal places, we multiply it by 1000. Next, we subtract them. Lastly, we divide both sides by 999 to get x as a **fraction**.

## What is .36 repeating as a fraction?

The **repeating** decimal 0.36363636. . . is written as the **fraction** 411 .

## What is .045 repeating as a fraction?

**045**, the very last digit is the “1000th” decimal place. So we can just say that .

**045**is the same as

**045**/1000. terms by dividing both the numerator and denominator by 5.

## What is .81 repeating as a fraction?

**9/11**.

## What is 0.7 Repeating as a fraction?

Repeating Decimal | Equivalent Fraction |
---|---|

0.2222 | 2/9 |

0.4444 | 4/9 |

0.5555 | 5/9 |

0.7777 | 7/9 |

## What is 0.3 Repeating as a fraction?

**fraction**. Answer: The decimal is converted to 4/5 as a

**fraction**. Problem 2: How do you convert 2.83 (3

**repeating**) to a

**fraction**?

## What is .15 repeating as a fraction?

0.151515. in **fraction** form is 5/33.

## How do you write 0.18 repeating as a fraction?

**1 Answer**

- We first let 0.18 be x .
- Since x is recurring in 2 decimal places, we multiply it by 100.
- Lastly, we divide both sides by 99 to get x as a fraction.

## Is Pi a rational number?

**Pi**is

**an irrational number**, which means that it is a real

**number**that cannot be expressed by a simple fraction. That's because

**pi**is what mathematicians call an “infinite decimal” — after the decimal point, the digits go on forever and ever. (These

**rational**expressions are only accurate to a couple of decimal places.)

## Is a repeating decimal a rational number?

**decimal number**that is

**repeating**can be written in the form a/b with b not equal to zero so it is a

**rational number**.

**Repeating decimals**are considered

**rational numbers**because they can be represented as a ratio of two integers.

## Does PI have repeating numbers?

**digits**of

**pi**never

**repeat**because it can be proven that

**π**is an irrational

**number**and irrational

**numbers**don't

**repeat**forever. . That means that

**π**is irrational, and that means that

**π**never repeats.

## Is 0 a rational number?

**rational number**. We know that the integer

**0**can be written in any one of the following forms. For example,

**0**/1,

**0**/-1,

**0**/2,

**0**/-2,

**0**/3,

**0**/-3,

**0**/4,

**0**/-4 and so on ….. Thus,

**0**can be written as, where a/b =

**0**, where a =

**0**and b is any non-zero integer.

## Is 7/12 a terminating decimal?

**decimal**expansions that are

**terminating**: 1/2, 3/4, 4/5, 7/8, 3/10, 15/16, 17/20, 23/25, 21/32, 13/40, 47/50, 45/64, 77/80, 87/100, 123/125, 5/12 is a repeating

**decimal**. A repeating

**decimal**is a

**decimal**that has a repeating digit.

## Is the fraction 1/3 equivalent to a terminating decimal?

**fractions**that do not

**terminate**like

**1/3**, 1/9, 1/7. in the denominator it will be a

**repeating**, non-

**terminating decimal**.

## What is the fraction for 0.1 repeating?

Fraction | Exact Decimal Equivalent or Repeating Decimal Expansion |
---|---|

1 / 7 | 0.142857142857142857 (6 repeating digits) |

1 / 8 | 0.125 |

1 / 9 | 0.111111111111111111 (1/3 times 1/3) or (1/3)^2 |

1 / 10 | 0.1 |

## What is repeating as a fraction?

**repeating**decimals are usually represented by putting a line over (sometimes under) the shortest block of

**repeating**decimals. Every infinite

**repeating**decimal can be expressed as a

**fraction**. Since 100 n and 10 n have the same fractional part, their difference is an integer.

## What is 1.5 Repeating as a fraction?

**repeating**decimal into a

**fraction**. Here's the mathematical way to derive it: Our number is a whole (1) plus a decimal portion (0.55555). So our original number 1.55555 is equal to 1+59 , which is 149 .

## Is a fraction a rational number?

**Rational Numbers**: Any

**number**that can be written in

**fraction**form is a

**rational number**. This includes integers, terminating decimals, and repeating decimals as well as

**fractions**. An integer can be written

**as a fraction**simply by giving it a denominator of one, so any integer is a

**rational number**.

## How do you turn 0.6666 into a fraction?

**Convert**the decimal number to a

**fraction**by placing the decimal number over a power of ten. Since there are 4 numbers to the right of the decimal point, place the decimal number over 104 (10000) . Next, add the whole number to the left of the decimal. Cancel the common factor of 6666 and 10000 .

## Is 9.373 a rational number?

**9.373**is a repeating decimal. Since we cannot see a bar on the digits after decimal, so our given

**number**is not a repeating decimal. We know that a

**number**is

**rational number**, when it can be represented as a fraction. Therefore, our given

**number**is a

**rational number**.