Scientific Notation and Standard Form

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Scientific Notation and Standard Form — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionMultiplying and Dividing Numbers in Scientific NotationConcept Practice

2 marks~3 minCriterion A

A satellite imaging system captures two circular coverage zones. The large zone has a radius of

9 \times 10^4

km and the small zone has a radius of

3 \times 10^2

km.

Using

A = \pi r^2

, calculate the ratio of the area of the large zone to the area of the small zone. Express your answer in scientific notation. [1]

A minimum coverage ratio of

1 \times 10^4

is required for the large zone to be classified as a primary zone. Justify whether the large zone meets this classification. [1]

Solutions

2QuestionMultiplying and Dividing Numbers in Scientific NotationAssessment Practice

6 marks~9 minCriterion C

The mass of Earth is

5.97 \times 10^{24}

kg and the mass of the Moon is

7.35 \times 10^{22}

kg.

Calculate the ratio of the mass of Earth to the mass of the Moon. Express your answer in scientific notation to three significant figures. [2]

Explain why scientific notation is appropriate when comparing astronomical masses, and explain how rounding to three significant figures affects the reliability of the ratio calculated in part (a). [2]

A scientist states: "This ratio means Earth is approximately 81 times more massive than the Moon, so the Moon has a negligible gravitational influence on Earth." Critique this statement, using your result from part (a) and your knowledge of real-world gravitational effects. [2]

Solutions

3QuestionConverting Between FormsConcept Practice

3 marks~5 minCriterion B

A spacecraft's distance from Earth is recorded using powers of

10

Power of $10$	$10^3$	$10^2$	$10^1$	$10^0$
Decimal equivalent	$1000$	$100$	$10$	$1$

State the number of zeros in the decimal equivalent of

10^3

and of

10^0

. [1]

Explain the relationship between the exponent in a power of

10

and the number of zeros in its decimal equivalent, using at least two values from the table to support your explanation. [1]

A scientist states: "Because $10^6$ has 6 zeros, a distance of $10^6$ km is exactly one million kilometres — large enough to matter in space navigation." Justify whether the scientist's reasoning about the number of zeros is mathematically correct, and explain what this means for expressing large distances in standard form. [1]

Solutions

4QuestionApplications in Science and Engineering ContextsAssessment Practice

6 marks~9 minCriterion D

An astronomer uses the distance modulus formula

d = 10^{\frac{m - M + 5}{5}}

to estimate the distance

d

(in parsecs) to a star, where

m

is the apparent magnitude and

M

is the absolute magnitude.

For a particular star,

M = 4.0

and the measured apparent magnitude is

m = 8.5 \pm 0.2

due to atmospheric distortion.

Calculate the distance to the star using

m = 8.5

. [2]

Calculate the distances corresponding to

m = 8.3

and

m = 8.7

. Express both answers in scientific notation to 3 significant figures. [2]

The astronomer claims the distance modulus formula gives a reliable estimate of this star's distance. Justify whether this claim is valid, using your results from parts (a) and (b) and considering that interstellar dust dims starlight. [2]

Solutions

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