Benchmark Numbers: Definition with Examples

What Are Benchmark Numbers?

A benchmark is defined as the standard or reference point based on which other things can be measured, or assessed, or compared. So, what is a benchmark in math? What does benchmark mean in math? 

Benchmark numbers are numbers using which other numbers or quantities can be estimated and compared. Benchmark numbers are usually multiples of 10 or 100, and sometimes multiples of 25. They are used to simplify the operations such as addition, subtraction, etc.

Here are some examples of benchmark numbers.

Definition of Benchmark Numbers

Benchmark numbers are numbers that are easy to add, subtract, multiply or divide. 

Any multiple of 10, 100, or multiples of 25 is considered as a benchmark number. 

Benchmark numbers are also known as “friendly” numbers. 

Examples: 10, 50, 1000, 80, 5000

A benchmark number is usually a multiple of 10, 100, 1000, etc., or a number having 0 at the ones place or any other decade number, such as 1, 20, 30, 40, etc. 

Let’s take a look at examples and non-examples of benchmark numbers.

Note: The most important benchmark numbers for young learners are 5 and 10. Because the number 10 plays such a huge role in our number system, and because $5 + 5 = 10$, it is very useful to develop relationships between the numbers 1 to 10.

List of Some Common Benchmark Numbers

Benchmark Numbers on a Number Line

Benchmark numbers help us to locate numbers, compare numbers. The following image shows benchmark numbers on the number line when counting by 1, 100, and 1000. Identify the benchmark numbers and locate any point on the number line.

Let’s understand benchmark numbers on a number line with examples.

1. Show benchmark numbers of 43 when counting by 10 on a number line.

The benchmark numbers of 43, when counting by 10, include 40 and 50. Observe the number line below to know how to locate 43 between its two benchmark numbers on the number line.

2. Show benchmark numbers of 160 when counting by 100 on a number line.

The benchmark numbers of 160 when counting by 100 include 100 and 200. Observe the number line below to know how to locate 160 between its two benchmark numbers on the number line. Notice that 160 itself is a benchmark number!

Addition Using Benchmark Numbers

Benchmark numbers make addition strategies simple. When adding two or more numbers, try to reach a benchmark number!

Let’s see how!

Example 1: $34 + 57 + 31 + 9$

Let’s break down this problem to reach benchmark numbers.

$34 + 57 + 31 + 9 = 30 + 4 + 50 + 7 + 30 + 1 + 9$

$= 110 + 11 + 10$

$= 130 + 1$

$= 131$

Refer to the following chart to reach the benchmark numbers faster. These number pairs make tens. 

You can also use them to make multiples of ten or even “hundreds” or “thousands.”

For example, if $2 + 8 = 10$, then 

           $22 + 8 = 30$

         $20 + 80 = 100$

     $200 + 800 = 1000$

There are many such combinations you can make!

Estimation Using Benchmark Numbers

Since the benchmark numbers are easy to add, subtract, multiply or divide easily, we can use them for estimation where some error in calculation is allowed.

Example 1: Estimating addition using benchmark numbers

Example 2: $31 \times 11 \approx 30 \times 10 \approx 300$

Let’s Sing!

When there are big numbers to compare,

Don’t let them give you a scare!

Bring in the benchmarks, to be fair!

Conclusion 

In this article we studied benchmark numbers. A benchmark number is any multiple of 10, 100, 1000, and sometimes 25 against which other numbers or quantities can be compared or accessed. 

Solved Examples on Benchmark Numbers

1. Identify the benchmark numbers: 43, 90, 100, 76, 500, 300

Solution:

Benchmark numbers in the given list are 90, 100, 500, 300.

2. How to solve  $54 + 32 + 67 + 13$ using benchmark numbers?

Solution:

Club the number pairs which make benchmark numbers or multiples of tens.

$54 + 32 + 67 + 13 = 50 + 4 + 30 + 2 + 60 + 7 + 10 + 3$

      $= 150 + 16$

      $= 166$

3. Which numbers should be added to the following numbers to get a benchmark number?
4. 4     b) 35     c) 313     d) 999

Solution:

Benchmark numbers are usually multiples of 10 or numbers having “0” at the ones place.

1. $4 + 6 = 10$
2. $35 + 5 = 40$
3. $313 + 7 = 320$
4. $999 + 1 = 1000$