Writing in standard form
Move the decimal point until a single non-zero digit is left in front: the number of places is the power, positive for large numbers and negative for small ones.
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Teaching guide: how to practise scientific notation
Scientific notation, called standard form in UK schools, writes a number as A × 10ⁿ, with a number in front between 1 and 10 and a power of 10, so that distances in space, the mass of an atom or the world's population can be read and compared at a glance. This free scientific notation worksheet generator builds A4 worksheets to write large and small numbers in standard form and as ordinary numbers, correct it, compare and order, multiply, divide, add and subtract, and solve problems with real data, from Grade 8 to Grade 10 (Years 9 to 11), with a step-by-step answer key.
Student worksheet 
Answer key As ordinary numbers
The way back: 7.2 × 10⁶ = 7,200,000 and 5 × 10⁻³ = 0.005. It shows that a negative power makes a number small, not negative.
Correcting it
35 × 10⁴ or 0.42 × 10⁶ are not in standard form: write the number in front as a power of 10 and add the powers.
Comparing and ordering
The power decides first: 2 × 10⁻³ is larger than 9 × 10⁻⁵. The sheets include the tricky cases and numbers to correct before ordering them.
Calculating
Multiplying and dividing with the laws of indices, and adding and subtracting by bringing both numbers to the same power. The answer key shows every step.
Real problems
Sunlight reaching Neptune, the mass of Jupiter, the red cells in our blood or the molecules in a glass of water, with real orders of magnitude.
Frequently asked questions about scientific notation worksheets
Which grades are these worksheets for?
Grades 8 to 10 (Years 9 to 11). Grade 8 writes large and small numbers in standard form; Grade 9 adds comparing, multiplying and dividing and sums with the same power; Grade 10 brings sums with different powers, calculations with three numbers and problems with atoms and cells.
What exactly is scientific notation?
A number written as A × 10ⁿ, where A is at least 1 and less than 10 (a single non-zero digit before the decimal point) and n is an integer. For example, 45,000,000 = 4.5 × 10⁷ and 0.00032 = 3.2 × 10⁻⁴. In the UK it is called standard form.
How do you add two numbers in standard form?
They need the same power: write the one with the smaller power with the larger power (3 × 10⁵ = 0.3 × 10⁶), add the numbers in front and keep the power. If the answer is not in standard form (10.1 × 10⁻³), correct it (1.01 × 10⁻²).
And how do you multiply and divide?
Multiply or divide the numbers in front and the powers of 10 separately: when multiplying, add the powers, and when dividing, subtract them. Then correct the answer if the number in front is 10 or more, or less than 1.
Do the problems use real data?
Yes, rounded as textbooks print them: the distances from the planets to the Sun, the speed of light, the mass of Earth, the size of a red blood cell or an atom, the mass of a hydrogen atom or the world's population. The data are chosen so that every calculation is exact.
What is in the answer key?
The answer to every exercise in standard form and the steps: how the number in front is corrected, the powers that are added or subtracted, the numbers brought to the same power and, in the problems, the data in standard form and the calculation.
What other worksheets go well with these?
The integer worksheets practise the signs of the powers, the decimal operations the calculations with the numbers in front, and the conversion factors and physics problems use standard form with units. Find every resource under maths worksheets.
Is any pupil data sent anywhere?
No. Worksheets are generated in your browser and templates are saved in your browser's memory.
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