Maths - Big Numbers, Small Tricks: Understanding Standard Form

Standard Form

Feb 04, 2025

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This lesson is all about Standard Form—a simple way to write very large or very small numbers without all the extra zeros!

https://uk.ixl.com/maths/year-10/convert-between-ordinary-numbers-and-standard-form

https://uk.ixl.com/maths/year-10/add-and-subtract-numbers-written-in-standard-form

https://uk.ixl.com/maths/year-10/divide-numbers-written-in-standard-form

Let's begin with a story.

The Story of Two Scientists and Their Shortcut.

Dr. Alex and Dr. Sam are busy in their laboratory, peering into a microscope to study bacteria.

The experiment is going well when suddenly, Dr. Sam’s phone rings.

"It's urgent! I need to step out," Sam says, rushing toward the door. "Just write down the results—I’ll check them later!"

Dr. Alex nods and turns back to the microscope.

"Wow! There are 4,500,000 bacteria here," Alex mutters. But there’s a problem—writing all those zeros will take forever!

Plus, Alex won’t be there when Dr. Sam returns, so the information needs to be quick and easy to understand.

Luckily, both scientists know the shortcut.

Instead of writing 4,500,000, Dr. Alex quickly writes:

👉 4.5 × 10⁶

Dr. Sam doesn’t need to be there to understand it—they both know the rules of Standard Form, so when Sam returns, he will immediately recognize that this means 4,500,000.

Meanwhile… Sam Has His Own Problem!

When Dr. Sam returns, he’s on his own. He checks another sample and finds 0.00032 grams of a rare chemical.

But now, Sam is in a hurry—he needs to get home to watch the football!

Writing all those zeros would slow him down, so he uses the same shortcut:

👉 3.2 × 10⁻⁴

Both scientists understand each other’s work without writing long numbers—that's the power of Standard Form!

Standard Form in Mathematics also called (Scientific Notation)

Standard Form is used to express very large or very small numbers in a shorter way. Instead of writing long numbers with lots of zeros, we use a simpler format.

Standard Form follows this pattern:

A number between one and ten multiplied by ten to the power of something.

This means:

The first number must be between one and ten (but it can have decimals).
The power of ten tells us how many places the decimal moves.

Examples:

1️⃣ Four thousand five hundred written in standard form:

The number is four thousand five hundred.
We write it as four point five multiplied by ten to the power of three.

2️⃣ Zero point zero zero seven two written in standard form:

We write it as seven point two multiplied by ten to the power of negative three.

Final Rule Summary for what we did above:

✅ Big numbers → Move decimal left → Positive exponent (power)
✅ Small numbers → Move decimal right → Negative exponent (power)

Lesson: Standard Form (with Jumps!)

Question 1: Convert 4,500,000 into Standard Form

Starting number: 4,500,000.
The decimal is at the end.

Now, we jump left (MOVE THE DECIMAL) until the number is between 1 and 10:

Now, move the decimal left step by step:

Corrected Version:

⬅ 450,000.0 (Jump 1)
⬅ 45,000.00 (Jump 2)
⬅ 4,500.000 (Jump 3)
⬅ 450.0000 (Jump 4)
⬅ 45.00000 (Jump 5)
⬅ 4.500000 (Jump 6) ✅ Stop!