Convert any number to standard form (scientific notation) or convert standard form back to an ordinary number. Step-by-step working shown for every conversion.
✓Last verified: April 2026 · Sources: BBC Bitesize, Khan Academy
Please enter a valid number (not zero).
Enter a whole number, decimal, or negative number
× 10
A must be between 1 and 10, n must be a whole number.
A is the coefficient (1 ≤ A < 10), n is the integer power of 10
Standard Form
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Standard Form
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A × 10^n
Coefficient A
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1 ≤ A < 10
Power n
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Exponent of 10
Ordinary Number
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Standard decimal
💡
📋 Step-by-Step Working
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Sources & Methodology
✓Standard form (scientific notation) rules are consistent with GCSE Mathematics requirements (Edexcel, AQA, OCR), US Common Core Standards, and Khan Academy curriculum references.
BBC Bitesize provides the authoritative UK GCSE curriculum definition of standard form including the rules A must satisfy (1 ≤ A < 10) and the integer requirement for n, which this calculator implements exactly.
Confirms the US scientific notation rules (identical to standard form) and the step-by-step conversion method implemented in this calculator's working section.
US Common Core Standard 8.EE.A.3 requires students to express numbers in scientific notation and perform operations with numbers in scientific notation — the core skill this calculator supports.
Method (Number to Standard Form): Find n = floor(log10(|x|)). Compute A = x / 10^n. If |A| >= 10 or |A| < 1, adjust n by 1. Result: A x 10^n where 1 ≤ |A| < 10 and n is an integer. Method (Standard Form to Number): Ordinary number = A x 10^n. If n > 0, move decimal right n places. If n < 0, move decimal left |n| places.
⏱ Last reviewed: April 2026
Standard Form Explained: Rules, Examples & How to Convert
Standard form (called scientific notation in the US) is a compact way of writing very large or very small numbers. Instead of writing 45,600,000 in full, you write 4.56 x 10^7. Instead of 0.000000032, you write 3.2 x 10^-8. The format always takes the form A x 10^n, where A is a number between 1 and 10, and n is any integer (positive, negative, or zero).
Standard form is essential in science, engineering, and computing because it makes calculations with extreme numbers manageable. The mass of the Earth is approximately 5.972 x 10^24 kg. The mass of a proton is 1.673 x 10^-27 kg. Multiplying these in standard form is straightforward — add the exponents, multiply the coefficients.
The Two Rules of Standard Form
A × 10^n where 1 ≤ A < 10 and n is an integer
Rule 1: A (the coefficient) must be at least 1 but less than 10. So 3.7 is valid, 0.37 is not, and 37 is not. Rule 2: n (the power of 10) must be a whole number (integer): ...,-3,-2,-1,0,1,2,3,...
To convert to standard form: Move the decimal until you have a number between 1 and 10. Count the moves — that is n. Left moves = positive n. Right moves = negative n.
Standard Form Examples — Quick Reference
Ordinary Number
Standard Form
A
n
45,600
4.56 × 10^4
4.56
+4
6,500,000
6.5 × 10^6
6.5
+6
300
3 × 10^2
3
+2
0.00045
4.5 × 10^-4
4.5
-4
0.000001
1 × 10^-6
1
-6
7
7 × 10^0
7
0
-25,000
-2.5 × 10^4
-2.5
+4
How to Convert Standard Form to Ordinary Numbers
To convert standard form back to an ordinary number, multiply A by 10^n. If n is positive, move the decimal point n places to the right — the number gets bigger. If n is negative, move the decimal point |n| places to the left — the number gets smaller.
Example: 3.7 x 10^5. Move decimal 5 places right: 3.70000 → 370,000. Example: 2.4 x 10^-3. Move decimal 3 places left: 0.0024. For very large n, you may need to add zeros as placeholders. For n = 8 with A = 1.23: 1.23 x 10^8 = 123,000,000.
Multiplying and Dividing Numbers in Standard Form
Multiplying: multiply the A values and add the n values. (3 x 10^4) x (2 x 10^3) = (3 x 2) x 10^(4+3) = 6 x 10^7. If the product of A values falls outside 1-10, adjust: (5 x 10^3) x (4 x 10^2) = 20 x 10^5 = 2 x 10^6.
Dividing: divide the A values and subtract the n values. (8 x 10^6) / (2 x 10^2) = 4 x 10^4. (3 x 10^2) / (6 x 10^5) = 0.5 x 10^-3 = 5 x 10^-4 (adjusted so A is in range).
💡 Common mistake: Students often write numbers like 0.45 x 10^3 or 45 x 10^2 — these are NOT standard form even though they equal 450. Standard form requires A to be between 1 and 10 (not including 10). The correct standard form for 450 is 4.5 x 10^2.
Frequently Asked Questions
Standard form (also called scientific notation in the US) is a way of writing numbers as A x 10^n, where A is between 1 and 10 (1 ≤ A < 10) and n is any integer. Examples: 3,000,000 = 3 x 10^6, and 0.00045 = 4.5 x 10^-4. It is used to represent very large or very small numbers compactly.
Move the decimal point until you have a number between 1 and 10. Count how many places you moved. If you moved left, n is positive (number was large). If you moved right, n is negative (number was small). Example: 45,600 - move decimal 4 places left to get 4.56. So 45,600 = 4.56 x 10^4.
Multiply A by 10^n. If n is positive, move the decimal n places right. If n is negative, move the decimal |n| places left. Example: 3.7 x 10^5 = 370,000 (move right 5). Example: 2.4 x 10^-3 = 0.0024 (move left 3).
0.00045 in standard form is 4.5 x 10^-4. Move the decimal 4 places right to get 4.5 (which is between 1 and 10). Since you moved right, n = -4. Check: 4.5 x 10^-4 = 4.5 x 0.0001 = 0.00045.
6,500,000 in standard form is 6.5 x 10^6. Move the decimal 6 places left to get 6.5. Since you moved left, n = +6. Check: 6.5 x 10^6 = 6.5 x 1,000,000 = 6,500,000.
Standard form and scientific notation are the same thing — just different names used in different countries. In the UK and Commonwealth countries it is called standard form. In the US it is called scientific notation. Both use A x 10^n where 1 ≤ A < 10 and n is an integer. The rules and format are identical.
Multiply the A values and add the n values. (A1 x 10^n1) x (A2 x 10^n2) = (A1 x A2) x 10^(n1+n2). Example: (3 x 10^4) x (2 x 10^3) = 6 x 10^7. If A1 x A2 is not between 1 and 10, adjust: (5 x 10^3) x (4 x 10^2) = 20 x 10^5 = 2 x 10^6.
Divide the A values and subtract the n values. (A1 x 10^n1) / (A2 x 10^n2) = (A1/A2) x 10^(n1-n2). Example: (8 x 10^6) / (2 x 10^2) = 4 x 10^4. If A1/A2 is outside 1-10, adjust the result into valid standard form.
0.000001 in standard form is 1 x 10^-6 (one millionth). Move decimal 6 places right to get 1.0. Since you moved right, n = -6. Check: 1 x 10^-6 = 0.000001.
Three rules: (1) Write as A x 10^n. (2) A must satisfy 1 ≤ A < 10 — at least 1 but less than 10. (3) n must be an integer (whole number). Numbers between 1 and 10 have n=0. Numbers ≥ 10 have positive n. Numbers < 1 have negative n. 0.45 x 10^3 is NOT standard form (A is too small); correct form is 4.5 x 10^2.
Make the powers of 10 equal first, then add the A values. Example: 3 x 10^5 + 2 x 10^4. Convert second term: 0.2 x 10^5. Now add: (3 + 0.2) x 10^5 = 3.2 x 10^5. If the result A is outside 1-10, readjust: 9.5 x 10^4 + 1.2 x 10^4 = 10.7 x 10^4 = 1.07 x 10^5.