Place Value and Decimals: math test solutions, Grade 5 – download the PDF

1 Place value and words / 3 pts

(a) Eighty and thirty-six thousandths. (1 pt)

(b) The 6 is in the thousandths place: \(0.006\). The 3 is in the hundredths place: \(0.03\). (1 pt)

(c) \(0.03 = 10 \times 0.003\), but compare with the 6: \(0.03 \div 0.006 = 5\). The value of the 3 is 5 times the value of the 6. (1 pt)

2 Powers of 10 / 3 pts

(a) Four zeros: \(10{,}000 = 10^4\). (1 pt)

(b) \(10^6 = 1{,}000{,}000\). (1 pt)

(c) \(5 \times 1{,}000 = 5{,}000\). (1 pt)

3 Powers of 10 and the decimal point / 4 pts

(a) Two places right: \(74\). (1 pt)

(b) Three places right: \(6{,}200\). (1 pt)

(c) Two places left: \(9.15\). (1 pt)

(d) Three places left with placeholder zeros: \(0.0036\). (1 pt)

4 Expanded form / 3 pts

(a) \(52.407 = 5 \times 10 + 2 \times 1 + 4 \times 0.1 + 0 \times 0.01 + 7 \times 0.001\), or \(50 + 2 + 0.4 + 0.007\). (2 pts)

(b) \(300 + 1 + 0.08 + 0.005 = 301.085\). (1 pt)

5 Comparing and rounding / 4 pts

(a) Tenths match (6); hundredths \(0 < 8\), so \(2.608 < 2.68\). (1 pt)

(b) \(0.053 < 0.305 < 0.35 < 0.5\). (1 pt)

(c) Nearest tenth: the hundredths digit is 6, so \(18.3\) (1 pt). Nearest hundredth: the thousandths digit is 4, so \(18.26\) (1 pt).

6 Bakery problem / 3 pts

(a) \(0.45 \times 100 = 45\) kg. (1 pt)

(b) \(45 \times 1{,}000 = 45{,}000\) g. (1 pt)

(c) \(45 \div 1{,}000 = 0.045\) kg per jar. (1 pt)