# Multiples of 100

One hundred may be one of the most essential and used numbers in the number system. This number is significant not only in the field of mathematics but also in the field of science, politics, and even religion.

In Latin, per cent means per hundred. Hence, the use of 100 as the basis of percentages – where 100% represents the full value. More so, centi- comes from the Latin word centum which means hundred. So, using the prefix centi- in centimeters means there are 100 centimeters in 1 meter. More so, the number of years in a **century** is 100. Meanwhile, in the field of Science, 100 represents the boiling temperature of water at sea level if it is in degree Celsius.

There are more significant things that this number has to offer. So, buckle up as we immerse ourselves in this holistic and extraordinary number!

## Multiples of 100 are 100, 200, 300, 400 …

If an integer is multiplied by 100, the products are considered multiples of 100. So, when a number is divided by 100, and the result is a whole number with a zero **remainder**, then that number is indeed a multiple of 100. Hence, a number that can be expressed as **100n**, where n is an integer, is a multiple of 100.

…but can we say that two numbers with a difference of 100 are already multiples of 100?

Not all numbers that have a difference of 100 are multiples of 100. Consider the numbers 120 and 220. These two numbers have a difference of 100, but when we divide it by 100, we will have a remainder of 20. One thing that we should never forget about multiples is – they should not have any remainder!

However, numbers like **100, 200, 300, 400, 500…** and so on are multiples of 100. Aside from the fact that the difference between any two consecutive numbers is 100, they will have a result of a whole number when divided by 100.

So, are you now enthusiastic about finding how we can generate any possible multiples of 100?

## How to find the multiples of 100?

Generating multiples of 100 is as easy as counting our 123s – the only difference is, we have to count by hundreds! But… before we teach you the fastest technique to find multiples of 100 – we’ll start with the **repeated addition** and **multiplication method!**

**Repeated addition**, also known as **skip counting**, is done by repeatedly adding 100 as many times as we want. You must always remember that the first and smallest positive multiple of any number is the number itself – 100.

Say, we are looking for the 3rd multiple of 100; we will simply add 100 three times. Hence, **100 + 100 + 100 = 300.** See… it’s so easy to do, right?

So, if someone asked you what is the 9th multiple of 100 and you have to use repeated addition, simply show them this: **100 + 100 + 100 + 100 + 100 + 100 + 100 + 100 + 100 = 900.**

Now, let’s try a quicker method!

For the second method, we will simply use **multiplication!**

We have defined multiples of 100 as an expression that can be defined by **100n** where n is an integer. So, if we are asked to get the 70th multiple of 100, we will simply multiply 100 by 70. **Hence, 100 x 70 = 7,000**. Therefore, the 70th multiple of 100 is 7,000!

…but let’s not forget that integers can be negative too! So, multiples of 100 can also be negative. Hence, if someone asked the negative 18th multiple of 100, we just need to get the product of 100 and -18. Hence, **100 x -18 = -1,800**. Therefore, the negative 18th multiple of 100 is -1,800.

Now that we’ve learned the two commonly used methods in finding multiples of 100, let’s take a look at the table below and compare the difference between the two discussed methods.

n^{th} Multiple | Repeated Addition | Multiplication |
---|---|---|

1^{st} multiple | 100 | 100 x 1 = 100 |

2^{nd} multiple | 100 + 100 = 200 | 100 x 2 = 200 |

3^{rd} multiple | 100 + 100 + 100 = 300 | 100 x 3 = 300 |

4^{th} multiple | 100 + 100 + 100 + 100 = 400 | 100 x 4 = 400 |

5^{th} multiple | 100 + 100 + 100 + 100 + 100 = 500 | 100 x 5 = 500 |

…but the fun is not done yet!

Now, let’s try this fastest and simplest way to get multiples of 100. We have said that generating multiples of 100 is like counting our 123s. So, here’s the trick, if we are asked to get the nth multiple of 100, we will just simply add two zeroes to it.

Say, we need to find the 15th multiple of 100. Using this technique, we will just add two zeroes after 15, hence 1,5**00**.

See, it’s very easy to remember, right?

## Did you know that…

…the sum of the first 9 prime numbers is 100?

Prime numbers are numbers whose only factors are 1 and itself. So, the first 9 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and 23. So if we add it all up, we will have a sum of 100!

Isn’t it amazing?

Now, can you think of any other cool facts about 100?

## List of First 30 multiples of 100

The table below shows the first 30 multiples of 100 that can be done by multiplying 1 to 30 by 100. While this list only shows the first 30 multiples, we can’t list all the multiples of 100 since numbers are infinite.

Product of 100 and a positive counting number | Multiples of 100 |
---|---|

100 x 1 | 100 |

100 x 2 | 200 |

100 x 3 | 300 |

100 x 4 | 400 |

100 x 5 | 500 |

100 x 6 | 600 |

100 x 7 | 700 |

100 x 8 | 800 |

100 x 9 | 900 |

100 x 10 | 1000 |

100 x 11 | 1100 |

100 x 12 | 1200 |

100 x 13 | 1300 |

100 x 14 | 1400 |

100 x 15 | 1500 |

100 x 16 | 1600 |

100 x 17 | 1700 |

100 x 18 | 1800 |

100 x 19 | 1900 |

100 x 20 | 2000 |

100 x 21 | 2100 |

100 x 22 | 2200 |

100 x 23 | 2300 |

100 x 24 | 2400 |

100 x 25 | 2500 |

100 x 26 | 2600 |

100 x 27 | 2700 |

100 x 28 | 2800 |

100 x 29 | 2900 |

100 x 30 | 3000 |

## Solving problems involving multiples of 100

Problems that occur in our daily lives may sometimes involve the use of mathematics – and applying what we learned in this article can help us fully understand how multiples of 100 can help us solve problems.

## Problem #1

Faye and Kenneth opened a savings account for their 1-year old daughter. Every month, they put $100 in the account. How much money will their daughter have after 5 years?

This problem wants us to calculate the money of Faye and Kenneth’s daughter after 5 years. It was stated that they put $100 in their daughter’s savings account every month. So, the first thing we need to solve is determining how much money they put in one year. This can be done by multiplying the money they put by the number of months in a year. Hence, **$100 x 12 months = $1200**. Thus, they saved $1200 each year.

Now, we just need to multiply it to the number of years. So, **$1200 x 5 years = $6000**. Therefore, after five years, Faye and Kenneth’s daughter’s bank account will have $6000.

## Problem #2

Stephanie bought a 100 meters by 100 meters lot for her parents. If each square meter costs $75, what is the total cost of the lot?

The problem asks us to compute the total cost of the lot Stephanie bought for her parents. Since each square meter costs $75, we need to find out first the total square meters of the lot. This can be done by computing the area of the 100 meters by 100 meters lot. Hence, **100 meters x 100 meters = 10 000 square meters**.

Now, we need to calculate the total amount Stephanie spent. So, **10 000 square meters x $75 = $750 000**.

Therefore, Stephanie bought that lot for $750 000. We’re pretty sure her parents are happy and proud of what Stephanie did!