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Year 10
Higher

Adding numbers in standard form

I can appreciate the mathematical structures that underpin addition of numbers represented in standard form.

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New
New
Year 10
Higher

Adding numbers in standard form

I can appreciate the mathematical structures that underpin addition of numbers represented in standard form.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. When adding numbers represented in standard form, place value is an important consideration.
  2. If the power of 10 is the same for both numbers, it is easy to add.
  3. Standard form calculations can be done using a calculator.

Keywords

  • Standard form - Standard form is when a number is written in the form A × 10^n, (where 1 ≤ A < 10 and n is an integer).

Common misconception

When adding numbers in standard form, pupils can also add the exponents of 10.

The use of the place value chart shows how the magnitude does not change to the sum of the powers of 10. The place value chart can support pupils to make the correct addition or subtraction of large or small numbers.

Using MWB, give pupils 5 x 10^5 and ask them to sum to numbers with different exponents to make 5 x 10^5. To support some pupils, they can convert to an ordinary number and write calculations. For more advanced, more use more significant figures. Extend further with the question 5 x 10^-5
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Match each number in standard form to its equivalent as an ordinary number.
Correct Answer:$$4.3\times10^{-4}$$ ,$$0.000 \text{ }43$$

$$0.000 \text{ }43$$

Correct Answer:$$4.4\times10^{4}$$ ,$$44 \text{ }000$$

$$44 \text{ }000$$

Correct Answer:$$4.3\times10^{4}$$ ,$$43 \text{ }000$$

$$43 \text{ }000$$

Correct Answer:$$4.3\times10^{8}$$,$$430 \text{ }000 \text{ }000$$

$$430 \text{ }000 \text{ }000$$

Correct Answer:$$4\times10^{4}$$,$$40 \text{ }000$$

$$40 \text{ }000$$

Q2.
Without a calculator, work out 39.38 + 9.3. The answer as a decimal is .
Correct Answer: 48.86
Q3.
Starting with the smallest, put these numbers into ascending order of size.
1 - $$1^{10}$$
2 - $$2^3$$
3 - $$10^1$$
4 - $$4^2$$
5 - $$5^2$$
6 - $$10^2$$
7 - $$5^3$$
Q4.
Match each number to its correct standard form equivalent.
Correct Answer:$$14.4\times10^{-5}$$ ,$$1.44\times10^{-4}$$

$$1.44\times10^{-4}$$

Correct Answer:$$0.54\times10^{-5}$$ ,$$5.4\times10^{-6}$$

$$5.4\times10^{-6}$$

Correct Answer:$$340\times10^{-5}$$ ,$$3.4\times10^{-3}$$

$$3.4\times10^{-3}$$

Correct Answer:$$34\times10^{-5}$$ ,$$3.4\times10^{-4}$$

$$3.4\times10^{-4}$$

Q5.
The Pacific Ocean has an approximate surface area of 166 000 000 km² and the Indian Ocean is approximately 73 000 000 km². What is the total surface area, in standard form, of these two oceans?
Correct answer: $$2.39\times10^{8}$$ km²
$$2.39\times10^{7}$$ km²
$$2.39\times10^{6}$$ km²
$$239\times10^{8}$$ km²
$$239\times10^{6}$$ km²
Q6.
Work out 0.04 m + 12 cm + 45 mm + 0.0008 km. The answer is centimetres.
Correct Answer: 100.5, 100.5 cm, 100.5cm

Exit quiz

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6 Questions

Q1.
Work out $$1.8\times10^5 + 5.6\times10^5 $$, giving your answer in standard form.
$$7.4\times10^10$$
Correct answer: $$7.4\times10^5$$
$$7.4\times10^6$$
$$7.4\times10^4$$
$$7.4\times10^{25}$$
Q2.
Work out $$3\times10^{-8} + 4.8\times10^{-8} $$, giving your answer in standard form.
$$7.8\times10^{8} $$
$$7.8\times10^{0} $$
$$7.8\times10^{-16} $$
Correct answer: $$7.8\times10^{-8} $$
Q3.
Work out $$1.4\times10^5 + 4\text{ }700\text{ }000$$, giving your answer in standard form.
$$4.84\times10^5$$
Correct answer: $$4.84\times10^6$$
$$4.84\times10^5$$
$$4.84\times10^3$$
Q4.
Work out $$4.9\times10^4 + 280\text{ } 000$$, giving your answer in standard form.
Correct answer: $$3.29\times10^5$$
$$3.29\times10^4$$
$$3.29\times10^3$$
$$3.29\times10^1$$
Q5.
Find the sum of $$9.38\times10^{10}$$ and $$1\text{ }300\text{ }000\text{ }000$$. Give your answer in standard form.
$$9.51\times10^{11}$$
$$95.1\times10^{10}$$
$$95.1\times10^{9}$$
$$9.51\times10^{9}$$
Correct answer: $$9.51\times10^{10}$$
Q6.
Work out $$2$$ mm + $$0.5$$ cm + $$2\times10^{-3}$$ m. Give your answer in metres.
Correct answer: $$9\times10^{-3}$$ m
$$9\times10^{-4}$$ m
$$9\times10^{-2}$$ m
$$9\times10^{-1}$$ m