Back to Exercise: Number Bases: Converting to and from Base 10

Exercises: Number Bases — Converting to and from Base 10

Work through each section in order. Show your work where indicated. In base $b$ , the only valid digits are $0$ through $b-1$ .

Grade 7·18 problems·~30 min·Uganda NCDC Primary 7 Mathematics·lesson·whole-numbers-03

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Recall / Warm-Up

In base 10, the number $345$ can be written as an expansion using powers of $10$ . Which expansion is correct?

$(3 \times 10^2) + (4 \times 10^1) + (5 \times 10^0)$

$(3 \times 10^1) + (4 \times 10^2) + (5 \times 10^0)$

$(3 \times 10^3) + (4 \times 10^2) + (5 \times 10^1)$

Evaluate $(2 \times 10^2) + (7 \times 10^1) + (4 \times 10^0)$ .

Fluency Practice

Which set of digits are the only valid digits in base 5?

$0, 1, 2, 3, 4$

$0, 1, 2, 3, 4, 5$

$1, 2, 3, 4, 5$

Convert $312_5$ to base 10 using the expand-and-add method.

$Place-value table for binary 1011 with column values 8, 4, 2, 1 above the digits and the products 8, 0, 2, 1 summing to 11$

Convert $1011_2$ to base 10 using the expand-and-add method.

Convert $1001_2$ to base 10.

$9$

$3$

$5$

$Repeated-division chain converting 82 to base 5, with remainders 2, 1, 3 top to bottom and an upward arrow showing they are read bottom to top as 312$

Convert $82$ to base 5 using repeated division. What is the result?

$312_5$

$213_5$

$321_5$

Convert $37$ to base 8 using repeated division. Write your answer as the base-8 numeral (digits only, no subscript).

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