Read the scale — answer key

1. SQ1 · Practice

Model answer. 5.4 cm. The key runs from the 1.0 cm mark to the 6.4 cm mark, so its length is 6.4 cm − 1.0 cm = 5.4 cm. The end of the ruler is worn, so measuring from the very end would add a zero error; starting at a clear mark and subtracting avoids it.

A full answer includes

• I chose 5.4 cm: 6.4 cm − 1.0 cm.
• I explained that the worn end means the zero mark is not at the end of the ruler, so starting there would add a zero error.

Also accept

• 5.4 cm (54 mm); starting at a clear mark avoids the error from the worn end.

Watch for

• “The length is the reading at the far end, 6.4 cm.” — That is only true when the object starts at zero. This key starts at the 1.0 cm mark, so subtract 1.0 cm.
• “Add the starting mark: 7.4 cm.” — The first centimetre of the ruler is not part of the key. Subtract the starting reading from the end reading.
• “6.4 mm, because the marks are millimetres.” — The numbered marks on this ruler are centimetres. And the key starts at 1.0 cm, so subtract: 6.4 cm − 1.0 cm = 5.4 cm.

2. SQ11 · Practice

Model answer. 8.0 cm = 80 mm. One coin = 80 mm ÷ 40 = 2.0 mm.

Checked automatically

• Thickness of one coin: 2.0 mm (2 significant figures)
  • Common wrong answer 0.2 : 0.20 is the thickness in centimetres. The answer must be in millimetres: 8.0 cm = 80 mm, so divide 80 mm by 40.
  • Common wrong answer 320 : You multiplied. Divide the height of the stack by the number of coins.
  • Common wrong answer 5 : You divided the number of coins by the height. Divide the height by the number of coins.

A full answer includes

• I changed 8.0 cm to 80 mm.
• I divided by the number of coins: 80 mm ÷ 40 = 2.0 mm.

Also accept

• 2.0 mm (0.20 cm is the same thickness, but the question asks for millimetres).

Watch for

• “8.0 ÷ 40 = 0.2, so one coin is 0.2 mm.” — 0.20 is the answer in centimetres, because the stack was measured in centimetres. In millimetres: 80 mm ÷ 40 = 2.0 mm.
• “Multiply: 8.0 × 40 = 320.” — One coin is much thinner than the whole stack, so divide the height of the stack by the number of coins.

3. SQ2 · Practice

Model answer. Eye level with the surface, reading the bottom of the meniscus. Put your eye level with the water surface and read the bottom of the curved surface, the meniscus. Looking from above or below makes the surface seem to sit against the wrong mark: that error is parallax.

A full answer includes

• I chose: eye level with the surface, reading the bottom of the meniscus.
• I named the error avoided: parallax, from looking at the scale from above or below.

Also accept

• Eye level, bottom of the meniscus; it avoids parallax error.

Watch for

• “Read the top edge, where the water touches the glass.” — The water climbs the glass at the edges, so the edges are higher than the true level. For water, read the bottom of the meniscus.
• “Look down from above so you can see the whole scale.” — From above, your line of sight crosses the scale at the wrong mark. That is parallax. Bring your eye level with the surface.

4. SQ3 · Practice

Model answer. 4.0 cm = 40 mm. One sheet = 40 mm ÷ 250 = 0.16 mm.

Checked automatically

• Thickness of one sheet: 0.16 mm (2 significant figures)
  • Common wrong answer 0.016 : 0.016 is the thickness in centimetres. The answer must be in millimetres: 4.0 cm = 40 mm, so divide 40 mm by 250.
  • Common wrong answer 6.25 : You divided the number of sheets by the thickness. Divide the thickness of the stack by the number of sheets.
  • Common wrong answer 62.5 : You divided 250 by 4.0. The thickness of one sheet is the stack’s thickness divided by the number of sheets.

A full answer includes

• I changed 4.0 cm to 40 mm.
• I divided by the number of sheets: 40 mm ÷ 250 = 0.16 mm.

Also accept

• 0.16 mm (0.016 cm is the same thickness, but the question asks for millimetres).

Watch for

• “4.0 ÷ 250 = 0.016, so one sheet is 0.016 mm.” — 0.016 is the thickness in centimetres, because the stack was measured in centimetres. Convert: 4.0 cm = 40 mm, and 40 mm ÷ 250 = 0.16 mm.
• “Divide the number of sheets by the thickness: 250 ÷ 40 = 6.25.” — That is how many sheets fit in each millimetre, not the thickness of one. Thickness of one = total thickness ÷ number of sheets.

5. SQ4 · Practice

Model answer. Volume = 32 cm³ (read at the bottom of the meniscus). Smallest division = 1 cm³.

A full answer includes

• I gave the volume as 32 cm³, from the bottom of the meniscus.
• I gave the smallest division as 1 cm³.

Also accept

• 32 cm³ (or 32 ml); 1 cm³.

Watch for

• “33 cm³, because that is where the water reaches the glass.” — The edges climb the glass, so they read too high. Read the bottom of the meniscus: 32 cm³.
• “The smallest division is 50 cm³, the size of the cylinder.” — 50 cm³ is the capacity. The smallest division is the gap between two neighbouring marks: 1 cm³.

6. SQ5 · Practice

Model answer. One sheet is about 0.1 mm thick, less than the ruler’s smallest division of 1 mm, so a direct reading is meaningless. A stack of 100 sheets is about 10 mm thick and easy to read. Any error in reading it, about half a millimetre, is shared out over 100 sheets when you divide, so the thickness of one sheet is found about 100 times more precisely.

A full answer includes

• I said one sheet is thinner than the smallest division of the ruler (1 mm), so it cannot be read directly.
• I explained that the error in reading the stack (about half a division) is shared over 100 sheets, so the error per sheet is about 100 times smaller.

Also accept

• The stack is big enough to read; the reading error is divided by 100 with the result.

Watch for

• “Measuring more sheets removes the error completely.” — The reading error is still there, but dividing by 100 makes it 100 times smaller per sheet. It is reduced, not removed.
• “It is better because you might pick a thin sheet by mistake.” — The sheets are identical. The real reason is the size of the reading compared with the smallest division of the ruler.

7. ST1 · Apply

Model answer. (a) 1.5 cm = 15 mm; diameter = 15 mm ÷ 30 = 0.50 mm. (b) For example: push the turns tightly together with no gaps, put the ruler right against the coil with your eye level with each end (no parallax), and start from a clear mark, not a worn end. Winding more turns makes the reading longer and the result more precise.

A full answer includes

• (a) I changed 1.5 cm to 15 mm and divided by 30: diameter = 0.50 mm.
• (b) I described one sensible step: turns tightly together with no gaps, eye level with the marks (no parallax), start at a clear mark rather than the worn end, or wind more turns.

Also accept

• (a) 0.5 mm; (b) any one valid improvement with its reason.

Watch for

• “Divide 30 by 1.5 cm.” — That gives the number of turns per centimetre. The diameter is the coil length divided by the number of turns.
• “One turn is the circumference of the pencil.” — Along the pencil, each turn takes up only the thickness of the wire, its diameter. The circumference is the distance round the pencil.